Question

The Carousel in the National Mall has 4 rings of horses. Kelly is riding on the inner ring, which has a radius of 9 feet. Maya is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is. In one rotation of the carousel, how much farther does Maya travel than Kelly? One rotation of the carousel takes 12 seconds. How much faster does Maya travel than Kelly?

Answer 1

Maya travels  $4.19 feet/sec$ faster than Kelly !

Difference in distance is : $106.76-56.52 = 50.24 feet$

Step-by-step explanation:

Here we have , The Carousel in the National Mall has 4 rings of horses. Kelly is riding on the inner ring, which has a radius of 9 feet. Maya is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is. We need to find In one rotation of the carousel, how much farther does Maya travel than Kelly . Let's find out:

Kelly is riding on the inner ring, which has a radius of 9 feet

Total distance traveled by Kelly is circumference of circle with radius 9 feet i.e.

⇒ $Distance = 2\pi r$

⇒ $Distance = 2(3.14) 9$

⇒ $Distance = 56.52feet$

Maya is riding on the outer ring, which is 8 feet farther out from the center than the inner ring .

Total distance traveled by Maya is circumference of circle with radius (8+9=17) feet i.e.

⇒ $Distance = 2\pi r$

⇒ $Distance = 2(3.14) 17$

⇒ $Distance = 106.76feet$

Therefore , Difference in distance is : $106.76-56.52 = 50.24 feet$

Now , Speed of both is give by

⇒ $Speed_k_e_l_l_y=\frac{56.52}{12} = 4.71 feet/sec$   And ,

⇒ $Speed_M_a_y_a=\frac{106.76}{12} = 8.90 feet/sec$

Faster Maya travels = 8.90-4.71 = 4.19

So , Maya travels  $4.19 feet/sec$ faster than Kelly !